1. Field of the Invention
This invention relates to a quantum computing method and a quantum computer using light.
2. Description of the Related Art
In recent years, tremendous research effort has been directed toward quantum computers, which execute calculations on the basis of the principle of quantum mechanics. In quantum computers, two quantum states, |0> and |1>, form the basis of information. The two states correspond to bit 0 and bit 1, which form the basis of information in present-day computers. In quantum computers, however, the two quantum states are called quantum bits (qubits) to distinguish them from bits in present-day computers, since superposition states, such as α|0>+β⊕1> (α and β are complex numbers), are used in the computing process.
It is known that any calculation can be executed by combining 1-qubit gates, each of which transforms one qubit, with 2-qubit gates, each of which transforms one of two qubits depending on the other. It is further known that a controlled-NOT (CNOT) gate, which leaves the latter qubit unchanged if the former qubit is |0> and exchanges |0> and |1> of the latter qubit if the former qubit is |1>, suffices for any calculation together with 1-qubit gates (M. A. Nielsen and I. L. Chuang, Quantum Information and Computation, Cambridge Univ. Press, 2000). These elementary gates are called universal gates. Use of universal gates enables any calculation to be executed. An attempt to realize a gate acting on three qubits or more (e.g., a quantum Toffoli gate, which is a 3-qubit gate and exchanges |0> and |1> of the one qubit only when the other two qubits are |1>|1>) by combining universal gates requires many gates and, therefore, the operation becomes complicated. To realize an actual quantum algorithm using many gates acting on three qubits or more, such as Shor's algorithm for prime factoring or Grover's algorithm for database searching, it is desirable that the gates acting on three qubits or more can be executed without decomposing into the universal gates.
Up to the present time, many methods of realizing 2-qubit gates have been presented. Pellizzari's method is known as the first one of the methods of executing a 2-qubit gate by connecting separate physical systems with an optical cavity (T. Pellizzari, S. A. Gardiner, J. I. Cirac, and P. Zoller, Phys, Rev. Lett. 75, 3788, 1995). Each of the physical systems used in the method is a three-level system having three energy levels each of which is doubly degenerate. A qubit is represented by degenerate two states of one of the two lower levels. The transition between the remaining one of the two lower levels and the upper level is resonant with the cavity mode. Since this method uses degenerate levels, when the user wants to operate the degenerate two states separately, the following problem arises: the user has to split the states by applying a magnetic field or an electric field in order to distinguish them in energy or use an optical selection rule unique to the materials used for the physical systems. Some methods of using a cavity without such a problem have been proposed (e.g., L. You, X. Y. Yi, and X. H. Su, Phys. Rev. A67, 032308, 2003). However, all of the conventional methods, including Pellizzari's method, relate to a 2-qubit gate, and a quantum computing method using a cavity which executes a gate acting on three qubits or more has not been proposed yet.